What is the Completely Factored Form of 2x³ + 4x² - x?

Solution:

Given that, 2x³ + 4x² - x

The factored form can be obtained by various methods.

2x³ + 4x² - x

The terms 2x³, 4x² and -x have a common factor of x:

2x³ + 4x² - x = x (2x² + 4x -1) 

Next, we will factorize (2x² + 4x -1) 

We will find the roots of (2x² + 4x -1)  to determine its factors using the quadratic formula.

x = [-4 ± √(4² - 4 × 2 × (-1))]/2 × 2

= [-4 ± √(16 + 8)]/4

= [-4 ± √24]/4

= [-2 ± √6]/2

The factors of (2x² + 4x -1) are [x - (-2 + √6)/2] and [x + (-2 - √6)/2]

The factors of 2x³ + 4x² - x are x, [x - (-2 + √6)/2], and [x + (-2 - √6)/2]

Hence, the completely factored form of 2x³ + 4x² - x is x [x - (-2 + √6)/2] [x + (-2 - √6)/2].

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What is the Completely Factored Form of 2x³ + 4x² - x?

Summary:

The Completely Factored Form of 2x³ + 4x² - x is x [x - (-2 + √6)/2] [x + (-2 - √6)/2].